Not sure if we're talking about the same thing? What you are is already there no matter how close or far you are to knowing yourself, however it is covered up by layers of delusion. These layers are also a part of what you are, they just happen to cover in fog (of war? lol) the bigger part of your nature. What people usually refer to as your "true nature".Is it really though? Or would this more apply to people who aren’t into Introspection? That one I would understand.
Introspection is something I have been practicing in some form since I was a young teenager. Examining oneself regularly and understanding oneself, at some point there’s nothing to really find and then it is more about creating yourself. Maybe the discipline is more your point? I don’t know if you are/how much you are aware of it. It’s a really great thing, the Buddhists highly insist on it too if I recall.
Regarding your second paragraph I'd argue there is always more to know about yourself. Maybe an exception could be a truly illuminated being. Personally I can't say whether that kind of human has ever existed or not. Although I admit I'd probably not be able to recognize such a thing anyway, it is kinda far from where I reside.
So in this venue, when you discover an emotion and/or thought that "controls" you, as time passes and you keep observing it... the frequency in which it comes lowers down until a point where it mostly doesn't ever return. However the "same" thing actually comes back in a more subtle way. And the exact same cycle just keeps repeating itself.
How far does the rabbit hole goes? As far as I can tell it just doesn't freaking end ^^
Of course a point comes where it is subtle enough that it mostly doesn't affect you or others, but it is still there. So... mmmh in practical terms I guess you could say you CAN know yourself, just not fully.
Personally I haven't met in person anyone who would fit the bill, even if we're talking in practical terms. Maybe some of those authors I mentioned are there, they certainly look the part.
All this is very tricky to write, even more so in English, and there are way too many nuances I haven't mentioned. The mind being a dual tool trying to make sense of a non-dual reality is probably the main one.
As a disclaimer, as far as I'm aware what I share isn't from any teachings but from personal experience. In general (and for a good reason) I don't really talk in terms of teachings.
If anyone felt a spark in curiosity feel free to PM me, we can arrange a voice talk when I can. That'd be way more productive (and fun) than writing about it.